The victory pushed the Jaguars (9-4) into sole possession of first place in the AFC South, with Tennessee losing at Arizona.
Bouye picked Wilson off twice while Ramsey intercepted Wilson late in the first half.
The Jaguars held a 10-0 lead in the third quarter, but Seattle came back with a 28-yard field goal and a 26-yard touchdown catch by Doug Baldwin with 7:32 remaining in the quarter.
Bortles broke the 10-10 tie on the first play of the ensuing drive. He found rookie receiver Keelan Cole for a 75-yard touchdown.
After getting a defensive stop, Jaydon Mickens returned a punt 72 yards to Seattle's 1-yard line and rookie Leonard Fournette scored from there for a 24-10 lead with 5:37 remaining in the third quarter.
Wilson made sure the Seahawks weren't done. He found receiver Paul Richardson for a 61-yard touchdown and hit receiver Tyler Lockett for a 74-yard touchdown.
Wilson eluded pressure to find Lockett, cutting the Jaguars lead to 30-24 with 3:42 left in the fourth quarter.
Seattle got the ball back with 2:39 left and went four-and-out as Wilson was sacked by Malik Jackson for an eight-yard loss on third-and-1.
Fournette broke a 13-yard run on third-and-11 to seal the victory.
Bortles threw for 268 yards on 18-of-27 passing with two touchdowns and no interceptions.
Fournette ran 24 times for 101 yards.
Wilson was 17 of 31 for 271 yards with three touchdowns. He also ran for 50 yards on five carries.
The game didn't seem headed for a shootout in the first half. The Jaguars took a 3-0 lead on a 38-yard field goal by Josh Lambo with 6:26 left in the first quarter.
Seattle had a chance to tie the game before halftime, but kicker Blair Walsh missed wide right from 38 yards with 16 seconds left in the second quarter.
The Jaguars went ahead 10-3 on an 18-yard touchdown catch by rookie Dede Westbrook early in the third quarter.
NOTES: Seattle DT Sheldon Richardson was ejected for throwing a punch in the final minute of the game when the Jaguars were in victory formation. Seattle DE Quinton Jefferson was ejected on the next play. ... Seattle's star tandem of linebackers, Bobby Wagner and K.J. Wright, left the game with injuries. Wagner sustained a hamstring injury, while Wright had a concussion. Jaguars WR Larry Pinkard left the game with a concussion. ... The Jaguars were without LB Telvin Smith (concussion) and WR Allen Hurns (ankle). Both were among the team's inactives. The Seahawks were without S Kam Chancellor (neck). ... The Jaguars announced a crowd of 64,431, their first sellout since the regular-season opener last year against Green Bay.